Exact closed-form expression for unitary spin-adapted fermionic singlet double excitation operators

TL;DR

This paper derives exact closed-form expressions for spin-adapted fermionic double excitation operators, facilitating efficient quantum circuit implementation and ensuring spin symmetry in quantum algorithms.

Contribution

It provides the first closed-form solutions for these operators, enabling improved efficiency and symmetry preservation in quantum computing applications.

Findings

Closed-form expressions for fermionic operators derived

Enhanced efficiency in quantum circuit implementation

Guarantees of spin symmetry in quantum algorithms

Abstract

We derive exact closed-form expressions for the matrix exponential of the anti-Hermitian spin-adapted singlet double excitation fermionic operators. These expressions enable the efficient implementation of such operators within unitary product state frameworks targeting conventional hardware, and allow for the implementation of ansatze that guarantee convergence to specific spin symmetries. Moreover, these exact closed-form expressions might also lay the groundwork for constructing spin-adapted circuits for quantum devices.